Blender Rigging process. Is skinning a must?
When you press Ctrl P and select With Automatic weights, blender sets up all the vertex groups for each bone. Blender uses the mesh closest to the bone for each vertex group.

In some cases With Automatic weights will work very well, if you have good bone placement. Other times you will have to tweak each bone's weight (the vertex group).

The unity tutorial talks about skinning specific bones to use with unity's Mecanim.